2021 AMC 10B Problem 13

Let n be a positive integer and d be a digit such that the value of the numeral \underline{32d} in base n equals 263, and the value of the numeral \underline{324} in base n equals the value of the numeral \underline{11d1} in base six. What is n + d ?

\textbf{(A)} ~10 \qquad\textbf{(B)} ~11 \qquad\textbf{(C)} ~13 \qquad\textbf{(D)} ~15 \qquad\textbf{(E)} ~16

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