Excel in math, science, and engineering

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If the cube root of \(\displaystyle 9\sqrt{3} + 11\sqrt{2}\) is of the form \(a\sqrt{b} + c\sqrt{d}\), where \(a,b,c,d\) are positive integers with \(b > d\). Find \(a^1 + b^2 + c^3 + d^4\).

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