1999 Cayley Problem 11

The time on a digital clock is 5:55. How many minutes will pass before the clock next shows a time with all digits identical?

\textbf{(A)}\ 71\quad \textbf{(B)}\ 72\quad \textbf{(C)}\ 255\quad \textbf{(D)}\ 316\quad \textbf{(E)}\ 436

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.