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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