Minimum too?

Algebra Level 5

\[\large (4x^2+3y)(4y^2+3x)+25xy\] If \(x,y\) are non-negative reals satisfy \(x+y=1\), let the sum of the maximum and the minimum value of the expression above be \(\dfrac{m}{n}\), where \(m\) and \(n\) are co-prime positive integers. Find \(m+n\)

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