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Here we study the electronic properties of cuprate/manganite interfaces. By means of atomic resolution electron microscopy and spectroscopy, we produce a subnanometer scale map of the transition metal oxidation state profile across the interface between the high $T_c$ superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ and the colossal magnetoresistance compound (La,Ca)MnO$_3$. A net transfer of electrons from manganite to cuprate with a peculiar non-monotonic charge profile is observed. Model calculations rationalize the profile in terms of the competition between standard charge transfer tendencies (due to band mismatch), strong chemical bonding effects across the interface, and Cu substitution into the Mn lattice, with different characteristic length scales., Comment: 11+7 pages, 3+2 figures