Matrices And Determinants

If \(\omega\) is an imaginary cube root of unity and \(\left| {\matrix{ {x + {\omega ^2}} & \omega & 1 \cr \omega & {{\omega ^2}} & {1 + x} \cr 1 & {x + \omega } & {{\omega ^2}} \cr } } \right| = 0\), then one of the values of x is