X, Y and Z

Algebra Level 1

$\begin{array} { l l l l l } & & X & Y& Z\\ & & X& Y& Z\\+&& &Y & Z \\\hline & 1 & 6 & 7 & 5\\ \end{array}$

$X,Y,$ and $Z$ are distinct single digits that satisfy the cryptogram above.

What is $X+Y+Z?$