i have a rear end question!

Ok my question is when running down the road and I give my dart gas it pulls to the left. It feels like it's in the rear end. Could my center section be going bad? At the track it hooks then pulls left and I break the tires loose. It's a 69 dart 8 3/4 w/741 case I think 3.91 gears. I have Ss springs and everything is tight on the car. It didn't do this until last year. It's no tire because I have changed tires. Please help. I do plan on a center section upgrade as soon as I can. Thanks Mark. I will post a video for the car running later.