OSN Proposal: Inequality

I proposed this problem to OSN 2009 but it was not selected.

For $a,b,c$ positive numbers such that $a+b+c=3$, prove that:

$2(a^{11} + b^{11} + c^{11}) + 3a^3b^3c^3(ab+bc+ca) \geq 5(a^4b^4 + b^4c^4 + c^4a^4)$