Recent advances in the field of left-handed materials (LHM) have renewed the interest for the study of the propagation properties in these materials. In particular, many works have been devoted to the study of the Veselago plate, which constitutes the simplest linear system based on LHM. Recently, Zharov and co-workers introduced a description of the nonlinear properties of LHM. In particular, they suggested that LHM could be used as the basis of power limiters, all optical switches, etc. In this communication, we consider a Fabry-Perot cavity filled with two materials having refractive indexes of opposite signs, and driven by an external coherent field. Using the well-known mean-field approximation, we derive a partial differential equation describing the bidirectional propagation of light in this optical cavity. In the absence of reflection at the interface between the LHM and the RHM, our model is similar to the well-known LL-model. However, an important difference that appears when considering LHM is that the sign of the diffraction term can be reversed by varying the geometry. Besides the bistable behaviour of the homogeneous response curve of the system, our study reveals the existence of modulational instability. The wavelength of the spatial dissipative structure emerging from that instability can be tuned continuously by varying the diffraction coefficient.