Herschel /PACS observations of 29 local ( Ultra- ) Luminous Infrared Galaxies , including both starburst and AGN-dominated sources as diagnosed in the mid-infrared/optical , show that the equivalent width of the absorbing OH 65 \mu m \Pi _ { 3 / 2 } J = 9 / 2 - 7 / 2 line ( W _ { \mathrm { eq } } ( \mathrm { OH 65 } ) ) with lower level energy E _ { \mathrm { low } } \approx 300 K , is anticorrelated with the [ C ii ] 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 L _ { \mathrm { IR } } / M _ { \mathrm { H 2 } } > 50 L _ { \odot } /M _ { \odot } mode as derived from previous CO line studies , the OH65 absorption shows a bimodal distribution with a discontinuity at L _ { \mathrm { FIR } } / M _ { \mathrm { H 2 } } \approx 100 L _ { \odot } /M _ { \odot } . 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 \Pi _ { 1 / 2 } J = 7 / 2 - 5 / 2 doublet ( E _ { \mathrm { low } } \approx 415 K ) , radiative transfer models characterized by the equivalent dust temperature , T _ { \mathrm { dust } } , and the continuum optical depth at 100 \mu m , \tau _ { 100 } , indicate that strong [ C ii ] 158 \mu m deficits are associated with far-IR thick ( \tau _ { 100 } \gtrsim 0.7 , N _ { \mathrm { H } } \gtrsim 10 ^ { 24 } cm ^ { -2 } ) , warm ( T _ { \mathrm { dust } } \gtrsim 60 K ) structures where the OH 65 \mu m absorption is produced , most likely in circumnuclear disks/tori/cocoons . With their high L _ { \mathrm { FIR } } / M _ { \mathrm { H 2 } } ratios and columns , the presence of these structures is expected to give rise to strong [ C ii ] deficits . W _ { \mathrm { eq } } ( \mathrm { OH 65 } ) probes the fraction of infrared luminosity arising from these compact/warm environments , which is \gtrsim 30 - 50 % in sources with high W _ { \mathrm { eq } } ( \mathrm { OH 65 } ) . Sources with high W _ { \mathrm { eq } } ( \mathrm { OH 65 } ) have surface densities of both L _ { \mathrm { IR } } and M _ { \mathrm { H 2 } } 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 .