find the points on the surface f(x,y,z)=1 that have a horizontal plane (ie a tangent plane horizontal to the xy plane)

where

f(x,y,z)= x^3 +y^34 -z^3.

I'm getting stuck as I can only find one point.

I got (0,0,-1) but this is by using a random vector I set as (0,0,-3z^2).