Complicated Equation!

Algebra Level 3

\[ \sqrt{1-2015x} + \sqrt{1+2015x} = \dfrac1{\sqrt{x+1}} + \sqrt{1+x} \]

Find the sum of all possible real values of \(x\) that satisfy the equation above.

Hint: \(x+y\geq 2\sqrt{xy} \).

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