Find the sum of all positive integers $x, y ,z$ such that $x \leq y \leq z$ and $x^{y} + y^{z} = z^{x}$

**Details and Assumptions:**

- If you get the solutions as ($1,3,10$) and ($2,3,16$). Then give your answer as the sum of all $x,y,z$ i.e. $1+3+10+2+3+16=35$.