I think the civil unrest is somehow part of a nexus of social (Civil Rights Movement, Prague Spring, May 1968 etc.) and economic (1973 oil Crisis) ‚crises‘ and environmental movements characteristic of the 1960s and 1970s. These seem to be in part closely intertwined, so I wouldn't characterise them as being coincidences. On the other part, by identifying one or several main causes one would be overly simplifying an extremely ample and complex phenomenon.

I'm therefore afraid I cannot give you a clear answer. Then again I'm far from being knowledgeable on the topic. My advice would be to seek for partial answers to your question by looking at small scale events or topics where social, economic and environmental issues seem to come together and influence each other. Personally I would recommend readings on general topics like environmental history (Joachim Radkau's „Nature and Power“ or John R. McNeill's „Something New Under the Sun“) or specific ones like the cultural history of aluminium (Mimi Sheller's „Aluminum Dreams“) to gain an insight into how consumer society or environmental issues and awareness played a part in the social upheavals of the 1960s and 1970s. Maybe someone could also give us reading tips on social, political and economic history?

Interestingly enough, opinions seem to be divided among some historians debating the question if the 1970s can be interpreted as historical turning point. (an example of such a debate, for German speakers: http://www.hsozkult.de/conferencereport/id/tagungsberichte-1699)

Big example is also South Africa, that was more seventies though. In those decades civil rights were being abused all over the world. Even today most protests are by under paid blue collar workers or students. Because what stops students from protesting they are old enough to know what is wrong and they have the time to fight for their future. I'm not the best at explaining but these are the years were the people stood up and said they mattered and the government didn't have full control.

Korea was relatively calm during the 60's. I say relatively because, while there were protests, they were usually small, short-lived, and didn't result in bloodshed or extreme violence

In April of 1960, there were protests against the government which led to the ouster of Syngman Rhee, but that was about it as far as major protests go. Student protestors were shot and many people were killed during the April Revolution. The April Revolution itself was sparked by the discovery of a body of a student who was killed by a tear gas canister in Masan during an earlier protest against electoral corruption.

A year later, in May of 1961, Park Chung-hee and his cadre overthrew the government in a coup, but there was little protest - the Rhee government had been corrupt, the Second Republic was locked in factionalism, and the efficiency of the junta meant the coup was over very rapidly.

The only other real protests were from the normalization of relations with Japan in 1965. The government negotiated, in secret, for reparations, loans, and technology transfers from Japan to make up for the 35 years of colonialism. The general public was not pleased with this as there was no official apology from the Japanese government.

If you want to see Korean protests, the 70's and 80's is where it's at. Park Chung-hee became much more authoritarian in the early 70's, resulting in his assassination by a close friend in 1979. In the fall of 1979, the protests in Busan were so bad that Park wanted to send in the military. The Korean CIA director cautioned against this while his chief of staff supported it. The argument came to a head and the KCIA director shot and killed the chief of staff, the president, as well as some body guards.

In the aftermath, Chun Doo-hwan (another military strongman) took over and continued the repression. However, the "386 generation" (in their 30's in the 90's, went to college in the 80's, and born in the 60's) had had enough and they protested heavily. The Gwangju Massacre happened in 1980, protests continued until 1987, and finally elections were announced and the transition to civilian rule began, just in time for the Olympics. During the 80's, the police arrested, tortured, and killed student protestors. During protests in '87, a student from Yonsei was hit in the head by a tear gas canister and eventually died. Lee Han-yeol had a funeral that was very well attended.

So, to answer your question about coincidence or underlying causes, the answer in regards to Korea is coincidence. Their protests in the 60's were linked specifically to the corruption of the First Republic and their anger at the Korea-Japanese treaty. In the 70's and 80's, their protests were directed at the harsh oppression of the military regimes.