2023 AMC 12B Problem 16

In Coinland, there are three types of coins, each worth 6, 10, and 15. What is the sum of the digits of the maximum amount of money that is impossible to have?

\textbf{(A)} 8 \qquad \textbf{(B)} 10 \qquad \textbf{(C)} 7 \qquad \textbf{(D)} 11 \qquad \textbf{(E)} 9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.