Square root Third Root

Algebra Level 4

If the cube root of 93+112\displaystyle 9\sqrt{3} + 11\sqrt{2} is of the form ab+cda\sqrt{b} + c\sqrt{d}, where a,b,c,da,b,c,d are positive integers with b>db > d. Find a1+b2+c3+d4a^1 + b^2 + c^3 + d^4.

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