My father grew up in a very rural part of the U.S. and had a very rural accent as a result (all his brothers still do). When he moved to Chicago as a young adult, he realized the social stigmas attached to his accent were hurting him and he set about to get rid of it. I'm not quite sure how he did it, he says he just read the dictionary and practiced the pronunciation guides for each word. But it was pretty total, he can't affect his native accent anymore even when he tries.
Here on the East Coast, there's actually quite a few dialect coaches who make their living teaching Asian immigrants how to pronounce all those terrible English 'L' and 'R' sounds (among others) they struggle with. The immigrant community here is pretty large, and the desire to succeed is very high (and their accents are often seen as barriers to success, often rightly so), so there's actually a fairly robust accent/dialect industry here.