Solving $(x^m+y^m-z^m)^n=(x^n+y^n-z^n)^m$

Question

If $m$ and $n$ are distinct positive integers then does the equation

$(x^m+y^m-z^m)^n=(x^n+y^n-z^n)^m$ $\space$has any solution , for $x,y,z$ , in positive integers with $x,y,z$ all not equal ?