Problem 5

Algebra Level 5

\[\frac{8a+3b+4(\sqrt{ab}+\sqrt{bc}+\sqrt[3]{abc})}{1+(a+b+c)^2}\]

Given that \(a,b,c\) are positive reals. If the maximum value of the expression above can be expressed as \(\large \frac{m}{n}\) where \(m,n\) are coprime integers.Find \(m+n\).


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