Didn't the Americans already destroy multiple Japanese cities using conventional bombs? Was there something completely different with using an atomic weapon to destroy a city vs. spending a couple of days just bombing the hell out of a city?
There are a lot of posts on this here already (here's one) — search for "Hasegawa" (the main author who argues it was mainly Russia) for a lot of discussion. The sort answer is: It is clear the Soviet invasion had a profound effect on many members of the high command, more of one than most people appreciate. But it's very hard to disentangle the events. One thing that does seem clear that Nagasaki did not significantly affect the position of the Japanese high command much.