# Inequality #2

Algebra Level 5

$\large \sum_{\text{cyc}(a,b,c)}\frac{\sqrt{a^3+b^3}}{ab+1} \geq \dfrac{3\sqrt{2}\sqrt[4]{m}}{4}.$

If the inequality above is true for all positive real numbers $$a,b,c$$ with constant $$m$$ such that $$a+b+c=abc$$, find the value of $$m$$.

×