While nearly all theoretical and computational studies of entangled polymer melts have focused on uniform samples, polymer synthesis routes always result in some dispersity, albeit narrow, of distribution of molecular weights (Đ_{M}=M_{w}/M_{n}∼1.02-1.04). Here, the effects of dispersity on chain mobility are studied for entangled, disperse melts using a coarse-grained model for polyethylene. Polymer melts with chain lengths set to follow a Schulz-Zimm distribution for the same average M_{w}=36 kg/mol with Đ_{M}=1.0 to 1.16, were studied for times of 600-800 μs using molecular dynamics simulations. This time frame is longer than the time required to reach the diffusive regime. We find that dispersity in this range does not affect the entanglement time or tube diameter. However, while there is negligible difference in the average mobility of chains for the uniform distribution Đ_{M}=1.0 and Đ_{M}=1.02, the shortest chains move significantly faster than the longest ones offering a constraint release pathway for the melts for larger Đ_{M}.