In this work, we assess the fundamental aspects of mutual miscibility of solvents by studying the mixing of two potential candidates, methanol and n-dodecane, for nonaqueous solvent extraction. To do so, H-1 NMR spectroscopy and molecular dynamics simulations are used jointly. The NMR spectra show that good phase separation can be obtained by adding LiCl and that the addition of a popular extractant (tri-n-butyl phosphate) yields the opposite effect. It is also demonstrated that in a specific case the poor phase separation is not due to the migration of n-dodecane into the more polar phase, but due to the transfer of the extractant into it, which is especially relevant when considering industrial applications of solvent extraction. With the aid of molecular dynamics simulations, explanations of this behavior are given. Specifically, an increase of all hydrogen-bond lifetimes is found to be consequent to the addition of LiCl which implies an indirect influence on the methanol liquid structure, by favoring a stronger hydrogen-bond network. Therefore, we found that better phase separation is not directly due to the presence of LiCl, but due to the "hardening" of the hydrogen-bond network.