We use resonant soft-x-ray scattering (RSXS) to study the electronic reconstruction at the interface between the Mott insulator LaMnO3 and the band insulator SrMnO3. Superlattices of these two insulators were shown previously to have both ferromagnetism and metallic tendencies [Koida, Phys. Rev. B 66, 144418 (2002)10.1103/PhysRevB.66.144418]. By studying a judiciously chosen superlattice reflection, we show that the interface density of states exhibits a pronounced peak at the Fermi level, similar to that predicted in related titanate superlattices by Okamoto et al. [Phys. Rev. B 70, 241104(R) (2004)10.1103/PhysRevB.70.241104]. The intensity of this peak correlates with the conductivity and magnetization, suggesting it is the driver of metallic behavior. Our study demonstrates a general strategy for using RSXS to probe the electronic properties of heterostructure interfaces.