Reversed Digit in Different Bases
The value of the two-digit number $\overline{ab}$ in base seven equals the value of the two-digit number $\overline{ba}$ in base nine. What is $a+b$?
\[
\textbf{(A)}\;7 \qquad
\textbf{(B)}\;9 \qquad
\textbf{(C)}\;10 \qquad
\textbf{(D)}\;11 \qquad
\textbf{(E)}\;14
\]