The dirty dime is a nickname for Tennessee. It comes from the lyrics of Blak Jak's "Ride & Swerve" though it was probably used colloquially before that. The components of the phrase come from the dirty south or the dirty dirty, and dime as in ten(nessee).
"I'm from the dirty dime, aka Tennessee" - Blak Jak
Dirty Dime is a nickname. A dime is a hot chick, known to be a 10/10. Dirty meaning this chick is very good in bed; satisfies her man and knows how to have fun.