let $f:R^3 -> R \ \ \ \ \ \ \ \ f(x,y,z)=x^4 + y^6 +z^8 \\$

$M = f^{-1}(1)$

Is M is diffeomorphic to a sphere $S^2$ ?

I tried to solve this problem, but I realized that I have no tools to solve it.

Constant rank theorem tells me M is a smooth 2 dimensional manifold, but does not tell me how it looks like.

And more generally, when $N = \{ x,y,z \in R^3 | ax^n + by^m + cz^l = 1\}$ is diffeomorphic to a sphere? What tools can I use to solve this problem?

Thank you for reading. Hoping get some shedding light in your reply.