Hey there! Sorry for getting to your question rather late. I'm going to take my best shot to give as complete an answer as I can:

In order to fully understand the Sino-Soviet split you have to go back all the way to the mid-1930s and the rise of communism in China, and the burgeoning relationship between Joseph Stalin and Mao Zedong. At the time the Chinese Communist Party (CCP) and the nationalist Guomindang (GMD) were locked in an uneasy alliance, forced to put aside their ideological concerns to deal with the direct threat of the Japanese invasion of China. Stalin, concerned with the Japanese threat to the Soviet Union, pushed for this alliance at the cost of Mao’s revolutionism. During these years Mao strengthened his position of the CCP’s military and political leader. This was made possible by the fact that Mao maintained close ties with the Soviet government and the Comintern. Indeed, while never looking to fully adopt the Soviet model of revolution, Mao and the CCP nonetheless considered the Soviet Union as a model upon which they could base their own state building. While Mao was always aware of the fact that Stalin considered the Chinese revolution to be expendable if it would mean Soviet security he nonetheless considered Stalin an example.

Due to the close relationship between the two leaders Mao and the CCP didn’t just experience the posthumous destalinization (the renunciation by the Soviet communist leaders of Joseph Stalin as a person and a leader, claiming that he had strayed from the path of true communism) as an ideological sin, they also considered it a personal slight. The policy had been developed entirely within the upper echelons of the Soviet communist party, catching the CCP entirely off guard. The Chinese were already working under the belief that Stalin's death made Mao the preeminent voice for world communism. Their response to destalinization was hesitant at first. Mao refused to follow Moscow's lead and completely repudiate Stalin, emphasizing the late dictator’s transgressions in failing to support the Chinese revolutions while simultaneously lauding his overall contributions to the spread of world communism. Furthermore, Mao downplayed Moscow’s wholesale rejection of cults of personality, choosing instead to differentiate between ‘correct’ (his own) and ‘incorrect’ (Stalin’s) expressions of leader-worship within communism. By 1959 assessing the extent of lingering Stalinist influence on Mao’s policies, rhetoric and cult of personality had become a growing concern to the Soviet embassy in Beijing. Mao also feared destalinization personally, worrying that after his death his rivals in the party would posthumously denounce him to further their own careers.

The close relationship between Stalin and Mao had also expressed itself in development aid from the Soviet Union to China, with the goal of helping China catch up to the economic and industrial standard of the Soviet Union. However, following the death of Stalin this aid became increasingly politicized. This was exacerbated by the policy choices Mao made in terms of trying to guide the economic development of China. The period between 1952 and 1980 was marked by a technological stagnation that left China unable to tap into the full production potential of its massive population. The closing of all educational institutions from primary schools to universities in 1966 would have profound long term repercussions for Chinese development. Furthermore, the economic and technological support that China was receiving from the Soviet Union had become a tool of political leverage for the latter, with support often being delayed or withheld completely in an attempt to strong-arm the Peoples’ Republic into compliance with the Soviet Union. The Great Leap Forward policies were met with especially harsh Soviet criticism, although this only served to reinforce Mao’s belief that the Soviet Union had strayed from the path of ideologically pure communism.

Even with growing famines Mao insisted on maintaining grain exports to the Soviet Union out of fear of losing face. By maintaining grain exports and isolating the Soviet embassy Mao initially managed to keep the famines hidden from the Soviets even as he became embroiled in a power struggle that would haunt CCP for more than a decade. Mao became obsessed with rooting out perceived ‘Khrushchevs at home and abroad’. This was not entirely unfounded. Loyalties within the CCP were hard to gauge, with leaders often showering the chairman with praise in private while providing blistering criticisms behind closed doors. The failure of the Great Leap Forward led Mao to launch his Cultural Revolution in order to fundamentally alter both Chinese society and CCP party culture. Red Guards closed down all major educational centres and it became official policy that children of urban professionals were to be ‘sent down’ to rural areas. The goal of this policy was to create a more egalitarian China, with children belonging to the former ‘exploiting class’ being disproportionally sent down. By cracking down on academia Mao managed to strengthen his position, but at the cost of further harming Chinese development.

Following World War II and the founding of the United Nations the Peoples' Republic of China found itself with a lack of international recognition, with the majority of non-Communist countries in stead recognizing the Republic of China (modern day Taiwan or Chinese Taipei) as the government that truly represented the Chinese people. This state was founded as a government in exile following the CCP's victory in mainland China. The ROC also held the UN security council seat, giving it quite a bit of political power on the international stage. The Soviet Union and the Peoples' Republic of China both wanted the PRC to assume the position the ROC held within the UN, but due to the institutional configuration of the UN that wasn't possible for the first fifteen years of the UN's existence. In the post-Stalin era however, with the rivalry between the Soviet Union and the Peoples' Republic.

One of the key stability checks within the United Nations is article 18 of the UN charter, which states that in the majority of matters being brought to vote a two-thirds majority is needed to pass a resolution. As a result of this restriction neither the communist nor the capitalist world had true control of the General Assembly. This effectively made it impossible to remove the Republic of China (ROC) from its seats in the General Assembly and Security Council in spite of the fact that it only governed only a fraction of the Chinese people. Nevertheless Albania, a close ally of the PRC, filed almost yearly resolutions written to allow the PRC to replace the ROC as the official Chinese representation within the General Assembly and Security Council.

This status quo was challenged by the wave of decolonization that took place during the 1960s, with many African nations becoming full members at this time. The fact that these nations dramatically altered the balance of power within the General Assembly is shown in the voting records on General Assembly resolution 2758, titled ‘Restoration of the lawful rights of the People's Republic of China in the United Nations’ with the overwhelming majority of the newly admitted post-colonial states voting in favour, providing the two-thirds majority needed. This was a blow to the United States. The two-thirds requirement had kept the PRC in relative isolation but the post-colonial General Assembly suddenly gave the annual Albanian resolution to allow the PRC to replace the ROC in the General Assembly and Security Council enough support. It meant that the PRC, at least within the UN, suddenly wielded as much authority as the Soviet Union did within the United Nations General Assembly. It meant that the Soviet Union was no longer the sole leading voice of communism within the UN.