I am profoundly deaf. If I can imitate accents of different parts of the world, so can you! You just have to develop awareness of the different sounds and the mouth positions to make them happen. Understand, I had speech therapy growing up, so it might benefit to have speech therapy in order to help you understand better how sounds are classified (velar, palatal, retroflex, dental, etc.), the differences (d is a voiced consonant, whereas t is exactly the same thing, only it is not voiced, and there are 4 ways to do the letter t, plus the double tt), and how to make these sounds by looking at mouth charts that help you how to position your tongue for various sounds. It is why I can imitate a country drawl, Native American Hispanic speakers, Indian speakers (whether English, Hindi, or Sanksrit), and some rudimental, easily-observed aspects of European language speakers.
If I can do it, you can too!