# Symmetric Conditions But Not Symmetric Equality

Algebra Level 5

$\large\sum_{\text{cyclic}(a,b,c)} \dfrac{a}{b+c}$

Let $$a,b$$ and $$c$$ be positive reals satisfying $a^2+b^2+c^2=\dfrac{11}{7}(ab+bc+ca) \; .$

If the sum of the minimum and maximum value of the expression above can be expressed as $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers, compute $$m+n$$.

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