AMC 12 2023b 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?

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