Liquid liquid phase diagrams of binary mixtures of the ionic liquid 1-dodecyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)amide (C(12)mimNTf(2)) with n-alkyl alcohols (decan-1-ol, undecan-1-ol, dodecan-1-ol, tetradecan-1-ol, hexadecan-1-ol, octadecan-1-ol, and eicosan-1-ol) are reported. Applying the cloud-point method on a set of samples, phase diagrams were obtained at atmospheric pressure in the temperature range of (280 to 423) K. The investigated systems show partial miscibility with an upper critical solution temperature between (288 and 352) K. With increasing chain length of the alcohols, the critical point is shifted toward higher temperatures and slightly higher concentrations, while the shape of the phase diagrams is nearly unaffected. Ising criticality is presumed for the numerical analysis of the phase diagrams. The analysis yields the data of the critical point and the parameters or the width and of the asymmetry which characterize the shape of the phase diagrams. The temperature dependence of the diameter of the phase diagrams, which describes the asymmetry, is not linear as presumed by the rectilinear diameter rule of Cailletet-Mathias but, as requested by scaling theories of critical phenomena, depends also on nonlinear, nonanalytical contributions that are the leading terms when approaching the critical solution point. For the mixture of C(12)mimNTf(2) + dodecan-1-ol the critical pond was determined independently using the equal-volume criterion. Taking into account the nonlinear temperature dependence of the diameter, the data of the critical point estimated from the fit of the phase diagram are in good agreement with those determined by the equal volume criterion.