In this manuscript, we studied the pure-cubic optical solitons with spatio-temporal and inter-modal dispersion in the absence of chromatic dispersion. To produce the analytical solution of the presentedmodel, we implemented two algorithms, namely, the Kudryashov auxiliary equation method and the new Kudryashov method. These two methods are based on the homogeneous balance constant. We acquired the dark, bright and singular solitons with choosing the appropriate parameter values. The threedimensional, contour and two-dimensional portraits of some of the obtained solutions were illustrated. Moreover, we investigated the effects of the coefficients of the model parameters on the soliton view with graphical representations.