Find the root

Algebra Level 3

\[\frac { 1 }{ \sqrt { { x }^{ 2 }+3 } } +\frac { 1 }{ \sqrt { 1+3{ x }^{ 2 } } } =\frac { 2 }{ x+1 } \]

Find the sum of all real \(x > -1\) satisfying the equation above.

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