Easy inequality

Algebra Level 3

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

If \(a,b\) and \(c\) are non-negative real numbers and the minimum value of the above expression is in the form \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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