\[\large p^x - y^3 =1\]
Solve the equation above over integral values of \(x,y,p\).
Details and assumptions:
Input the answer as the sum of possible answers. As an explicit example, input 12 if the only triplet satisfying the equation is \((1,1,10)\) .
\(p\) is a prime.
\(x,y\) are positive integers.