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Algebra Level 4

\[ \large \left( x+ \sqrt{x^2+\sqrt{2015}}\right)\left( y+ \sqrt{y^2+\sqrt{2015}}\right) = \sqrt{2015} \]

If \(x\) and \(y\) are real numbers that satisfy the equation above, find the value of \(S\) such that \(S = x+y\).

Hint: Multiply both sides by with \( \left( \sqrt{x^2+\sqrt{2015}} - x\right) \) and \( \left( \sqrt{y^2+\sqrt{2015}} - y\right) \).

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