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Algebra Level 5

21x3+5y2+2016z221x^3+5y^2+2016z^2

Given that x,yx,y and zz are positive real numbers satisfying xyz=57033xyz=\dfrac{5\sqrt{70}}{\sqrt[3]{3}}. It is known that the minimum value of the above expression is aba\sqrt{b}, where aa and bb are positive integers with bb square-free. Find a+ba+b.

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