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Algebra Level 5

\[21x^3+5y^2+2016z^2\]

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

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