Same Coefficients

Algebra Level pending

Solve the following system for distinct \(x\), \(y\), and \(z\).

\[\begin{cases} 5732x+2134y+2134z = 7866 \\ 2134x+5732y+2134z= 670 \\ 2134x+2134y+5732z= 11464 \end{cases} \]

What is \(x+y+z=\) ?

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