The main target of this work is implementing multiple accurate cubic optical solitons for the nonlinear Schrödinger equation in the presence of third-order dispersion effects, absence of the chromatic dispersion. The emergence cubic optical solitons of the proposed model are extracted for the Kerr-Law and Power-Law nonlinearity in the framework of two distinct techniques, the first one is the extended simple equation method (ESEM), while the other is the solitary wave ansatz method (SWAM). These cubic optical solitons for the Kerr-Law and Power- Law nonlinearity have been extracted successfully at the same time and parallel via these two different techniques. A good comparison not only between our achieved results by these two manners but also with that achieved previously has been extracted.