Problem maximized!

Algebra Level 4

\(x,y\) and \(z\) are positive reals satisfying \(x+y+z = 10\).

If the maximum value of \(xyz + xy + yz + zx\) can be expressed as \( \dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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