Not so easy

Algebra Level 3

\[ \dfrac a{b+c} + \dfrac b{a+c} + \dfrac c{a+b} \]

If \(a,b\) and \(c\) are positive real numbers, find the minimum value of the expression above. If this value can be expressed as \(\dfrac mn\), where \(m\) and \(n\) are coprime positive integers, submit \(m+n\) as your answer.

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