When I'm lifting using dumbells, on my last set I often hit failure a rep or two sooner on my left arm than my right.
I was hoping someone could help suggest how to correct the imbalance. Do I need to work the left more often? Extra set with the left arm?
Any advice would be appreciated.

I'd continue with the dumbbells (as opposed to barbells) and even add in machines that allow you to work one arm at a time. Also, you said arm as opposed to specifying a muscle group or exercise on which you are failing. If you know where your imbalance is (i.e. front delt), I'd add in some isolation exercises for that muscle group. Also, I'd start my sets with the weaker side first, allowing it to determine my rep count. Then on the stronger side I'd stop at the same point as the weaker side. This way over time both sides will be in balance. Hope that helps.

Yup, working the right enough for it to keep it's current strength until the left catches up is exactly what I was told by a friend who's a personal trainer. Once both are able to lift that weight, then you can increase.