Vieta root jumping is a descent method that occurs when you have to solve a Diophantine equation whose solutions have a recursive structure. Popular in advanced math olympiad number theory problems.

If \(x\) and \(y\) are non-zero real numbers satisfying the system of equations

\[\begin{cases} x-y= 24, \\ x^2-2xy-y=24, \end{cases}\] what is the value of \(x+y\)?

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