Depth of some special monomial ideals

Let I ) J be two squarefree monomial ideals of a polynomial algebra over a eld. Suppose that I is generated by one squarefree monomial of degree d > 0, and other squarefree monomials of degrees d + 1. If the Stanley depth of I=J is d + 1 then almost always the usual depth of I=J is d + 1 too.