Sequential roots

Algebra Level 4

a,ba, b and cc are positive real numbers satisfying a+b+c=100 a + b + c = 100 . The maximum value of

a+ab+abc3 a + \sqrt{ab} + \sqrt[3]{abc}

can be expressed as mn \dfrac{m}{n} , where mm and nn are coprime positive integers. What is the value of m+nm+n?

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