For what $t$ is $M_t=\{(x,y,z):x^2+y^2+z^2=1,x^2-y^2+tz^3=1\}$ differential manifold?

Question

For which $t$ is followins set a differential manifold $$ M_t=\{(x,y,z):x^2+y^2+z^2=1,x^2-y^2+tz^3=1\} $$ I tried to analyze possible determinants of $2\times2$ matrixes from $ \begin{bmatrix}2x & 2y & 2z \\2x & -2y & 3tz^2 \end{bmatrix}$ but couldn't obtain acceptable result.