This is an exercise for knowing the non-system units. You'll do well just reading about them all.
Still, the formula is umbiguous. It is not clear in what system it is used. It is not difficult to form charge there as e2/]hbar c = alpha in Gauss system. But in SI there is yet some \epsilon_0 there.
Looking at the Remi's answer I see I read it completely differently. Wavenumbers are immidiately electronvolts for me. Not the length unit but the energy units. But, since this is not linear one cannot be sure what is meant