Balancing a drum is not for the faint of heart. it is a professional job.
IF in fact the drum is out of balance some shops may have the ability to do it, it is done by welding metal to the drum in an area where it won't be bothered.
Another posibility is the drum may need to be turned or it may be out of round.
Again a professional who has the tools (And sadly those are rare these days) is needed to figure it out... I can not, and do not know off hand anyone who can, but your Tire Professional MIGHT. I stress MIGHT. I know one weld shop that might too but less you are in metro Detroit,, Not much joy there. (Marty's On Telegraph between 5 and 6 mile I as I recall)
