I have a 2003 5.9 cummings 3500 and the belt broke and after replacing it the truck hesitates and sometimes dies.
When I went to start it back up I had to let it crank for at least 10-15 seconds before it started. That concerned me a bit. When I'm driving dont even think about accelerating fast because it will stall. I have to take it nice and easy or it's very pronounced. It still does it but less noticable.
After saying all that, could the belt have damaged the crank sensor? I've read that when it breaks the belt hits the sensor and the truck won't start. Mine started but is not acting like it should.

 

First we need to know what a "cummings" is....

 

I would question WHY the belt broke. Is something seizing up in the belt path? That could be alternator, water pump, etc... which are things that affect running. (I don't know your engine).Take the belt off and turn things by hand. The only thing that offers resistance should be the crank.

 

The belt was just worn. I knew it was and got lazy and forgot to change it. Everything spins fine. Truck was running just fine before the belt broke.