Crazy indices

Algebra Level 4

Find the sum of all positive real \(x\) that satisfies

\(\sqrt{x}( 9^{\sqrt{x^{2}-3}} - 3^{\sqrt{x^{2}-3}}) = 3^{2\sqrt{x^{2}-3}+1} - 3^{\sqrt{x^{2} - 3}+1} + 6\sqrt{x} - 18\),

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