We define a non-degenerated Monge-Ampere structure on a 6-manifold associated with a Monge-Ampere equation as a couple (\Omega,\omega), such that \Omega is a symplectic form and \omega is a 3-differential form which satisfies \omega\wedge\Omega=0 and which is non-degenerated in the sense of Hitchin. We associate with such a couple an almost (pseudo) Calabi-Yau structure and we study its integrability from the point of view of Monge-Ampere operators theory. The result we prove appears as an analogue of Lychagin and Roubtsov theorem on integrability of the almost complex or almost product structure associated with an elliptic or hyperbolic Monge-Ampere equation in the dimension 4. We study from this point of view the example of the Stenzel metric on T*S^3.