# Problem 8

Algebra Level 5

$\frac{a}{b^3+c^3+1}+\frac{b}{c^3+a^3+1}+\frac{c}{a^3+b^3+1}$

Given that $$a,b,c$$ are non-negative and $$a+b+c=1$$. Find the sum of the minimum and maximum value.