Solve the system of linear equations by elimination and find the sum of ordered triple $x+y+z$. \[ \left\{\begin{array}{l} -x+5 y-5 z=-36 \\ -5 x+6 y+2 z=-18 \\ -2 x+5 y+2 z=0 \end{array}\right. \]

Step 1 ：Define the system of linear equations as follows: \[ \left\{\begin{array}{l} -x+5 y-5 z=-36 \ -5 x+6 y+2 z=-18 \ -2 x+5 y+2 z=0 \end{array}\right. \]

Step 2 ：Solve the system of equations to find the values of \(x\), \(y\), and \(z\). The solution is \(x = 6\), \(y = 0\), and \(z = 6\).

Step 3 ：Find the sum of the solutions. The sum of the solutions is \(6 + 0 + 6 = 12\).

Step 4 ：Final Answer: The sum of the ordered triple \((x, y, z)\) is \(\boxed{12}\).