The oxidation and spin states of the three cations in Co0.6Fe0.9Mn1.5O4, showing a nano-checkerboard structure, were investigated using nuclear magnetic resonance (NMR) and x-ray absorption spectrocopy (XAS) techniques. Comparison of the Co, Fe and Mn 2p XAS spectra with reference spectra suggests the presence of Co2+, Co3+, Fe3+, Mn2+ and Mn3+. Four distinctive NMR peaks were observed in the wide spectral range of 50-610 MHz. The external field dependence of the peaks and comparison of the peaks with those in other spinels also confirm the existence of the cation oxidation states suggested by XAS. Analysis of these results, combined with the magnitude of saturated magnetization, indicates an average chemical formula of (Mnx2+Co1-x2+)(A)[Cox-0.43+Mn1.5-x3+Fe0.93+](B)O-4 with x similar to 0.9. Thus, Co0.6Fe0.9Mn1.5O4 appears to be a ferrimagnet with the majority spins from Fe3+, Co2+ and Mn3+ and the minority spins from Co3+ and Mn2+.