Nested fight back!

Algebra Level 5

\(x = \sqrt{19} + \dfrac{91}{{\sqrt{19}+\dfrac{91}{{\sqrt{19}+\dfrac{91}{{\sqrt{19}+\dfrac{91}{{\sqrt{19}+\dfrac{91}{x}}}}}}}}}\)

Find \(A^2_{}\) , where \(A^{}_{}\) is the sum of the absolute values of all roots of the equation above.

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