Having an accent is not the same as being unable to speak proper english! Yes lots of doctors have Indian accents, but they speak ENGLISH, and some of them better than most americans.
What the poor blacks often speak is not anything remotely resembling proper english. Bad Grammar is not an accent.
Improving one's grammar invariably moves one's accent closer to Standard English and mitigates the unintelligibility of the ghetto or swamp accent. To improve your grammar you have to begin to think a bit about what you are saying and you will be conscious that what you are doing is trying to be understood by people beyond your old neighborhood. You can't help improving your accent when you set out to improve just your grammar.