MathNet 2011 Question 22

Let $A$ and $B$ be disjoint nonempty sets with $A \cup B=\{1,2,3, \ldots, 10\}$. Show that there exist elements $a \in A$ and $b \in B$ such that the number $a^{3}+a b^{2}+b^{3}$ is divisible by 11.