Complicated Equation!

Algebra Level 3

12015x+1+2015x=1x+1+1+x \sqrt{1-2015x} + \sqrt{1+2015x} = \dfrac1{\sqrt{x+1}} + \sqrt{1+x}

Find the sum of all possible real values of xx that satisfy the equation above.

Hint: x+y2xyx+y\geq 2\sqrt{xy} .

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