The secret for the Soviets/Russians isn't so much their training, of which the mainstay was the Botvinnik School which most of their top GMs and all of their top trainers contributed to, but instead their dedication to finding the talent in the first place. Chess is traditionally very popular there, and not in the very casual way we do in the West where nearly everyone knows the moves but few take it remotely seriously. So they scout out the promising schoolkids - and they make sure all the kids play and some reasonably strong adults are watching for the signs of aptitude.
The Russians find all their great players, whereas many of ours never find they even have talent and instead go on to useless lives of science, medicine, technology, finance, astrophysics, etc.
+1
lol @ tal