AMC 12 2012b Problem 11

In the equation below, $A$ and $B$ are consecutive positive integers, and $A$, $B$, and $A+B$ represent number bases: $$132_A+43_B=69_{A+B}.$$ What is $A+B$?

\textbf{(A)}\ 9 \textbf{(B)}\ 11 \textbf{(C)}\ 13 \textbf{(D)}\ 15 \textbf{(E)}\ 17