The ambiguous origin of the [CII] 158um line in the interstellar medium complicates its use for diagnostics concerning the star-formation rate and physical conditions in photodissociation regions. We investigate the origin of [CII] in order to measure the total molecular gas content, the fraction of CO-dark H_2_ gas, and how these parameters are impacted by environmental effects such as stellar feedback. We observed the giant HII region N 11 in the Large Magellanic Cloud with SOFIA/GREAT. The [CII] line is resolved in velocity and compared to HI and CO, using a Bayesian approach to decompose the line profiles. A simple model accounting for collisions in the neutral atomic and molecular gas was used in order to derive the H_2_ column density traced by C^+^. The profile of [CII] most closely resembles that of CO, but the integrated [CII] line width lies between that of CO and that of HI. Using various methods, we find that [CII] mostly originates from the neutral gas. We show that [CII] mostly traces the CO-dark H_2_ gas but there is evidence of a weak contribution from neutral atomic gas preferentially in the faintest components (as opposed to components with low [CII]/CO or low CO column density). Most of the molecular gas is CO-dark. The CO-dark H_2_ gas, whose density is typically a few 100s/cm^3^ and thermal pressure in the range 10^3.5-5^K/cm^3^, is not always in pressure equilibrium with the neutral atomic gas. The fraction of CO-dark H_2_ gas decreases with increasing CO column density, with a slope that seems to depend on the impinging radiation field from nearby massive stars. Finally we extend previous measurements of the photoelectric-effect heating efficiency, which we find is constant across regions probed with Herschel, with [CII] and [OI] being the main coolants in faint and diffuse, and bright and compact regions, respectively, and with polycyclic aromatic hydrocarbon emission tracing the CO-dark H_2_ gas heating where [CII] and [OI] emit. We present an innovative spectral decomposition method that allows statistical trends to be derived for the molecular gas content using CO, [CII], and HI profiles. Our study highlights the importance of velocity-resolved photodissociation region (PDR) diagnostics and higher spatial resolution for HI observations as future steps.