Herschel/PACS observations of 29 local (ultra) luminous infrared galaxies, including both starburst and active galactic nucleus (AGN) dominated sources as diagnosed in the mid-infrared/optical, show that the equivalent width of the absorbing OH 65 mu m.3/2 J = 9/2-7/2 line (Weq(OH65)) with lower level energy Elow 300 K, is anticorrelated with the [Cii] 158 mu m line to far-infrared luminosity ratio, and correlated with the far-infrared luminosity per unit gas mass and with the 60-to-100 mu m far-infrared color. While all sources are in the active LIR/MH2 > 50L /M mode as derived from previous CO line studies, the OH65 absorption shows a bimodal distribution with a discontinuity at LFIR/MH2 100L /M . In the most buried sources, OH65 probes material partially responsible for the silicate 9.7 mu m absorption. Combined with observations of the OH 71 mu m.1/2 J = 7/2-5/2 doublet (Elow 415 K), radiative transfer models characterized by the equivalent dust temperature, Tdust, and the continuum optical depth at 100 mu m, t100, indicate that strong [C ii] 158 mu m deficits are associated with far-IR thick (t100 0.7, NH 1024 cm-2), warm (Tdust 60 K) structures where the OH 65 mu m absorption is produced, most likely in circumnuclear disks/tori/cocoons. With their high LFIR/MH2 ratios and columns, the presence of these structures is expected to give rise to strong [C ii] deficits. Weq(OH65) probes the fraction of infrared luminosity arising from these compact/warm environments, which is 30%-50% in sources with high Weq(OH65). Sources with high Weq(OH65) have surface densities of both LIR and MH2 higher than inferred from the half-light (CO or UV/optical) radius, tracing coherent structures that represent the most buried/active stage of (circum) nuclear starburst-AGN co-evolution.