Surfactant molecules self-assemble in aqueous solutions to form various micellar structures such as spheres, rods, or lamellae. Although phase transitions in surfactant solutions have been studied experimentally, their molecular mechanisms are still not well understood. In this work, we show that molecular dynamics (MD) simulations using the coarse-grained (CG) MARTINI force field and explicit CG solvent, validated against atomistic MD studies, can accurately represent micellar assemblies of cetyltrimethylammonium chloride (CTAC). The effect of salt on micellar structures is studied for aromatic anionic salts, e.g., sodium salicylate, and simple inorganic salts, e.g., sodium chloride. Above a threshold concentration, sodium salicylate induces a sphere to rod transition in the micelle. CG MD simulations are shown to capture the dynamics of this shape transition and support a mechanism based on the reduction in the micelle-water interfacial tension induced by the adsorption of the amphiphilic salicylate ions. At the threshold salt concentration, the interface is nearly saturated with adsorbed salicylate ions. Predictions of the effect of salt on the micelle structure in different CG solvent models, namely, single-site standard water and three-site polarizable water, show qualitative agreement. This suggests that phase transitions in aqueous micelle solutions could be investigated by using standard CG water models which allow for 3 orders of magnitude reduction in the computational time as compared to that required for atomistic MD simulations.