Square root Third Root

Algebra Level 4

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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