2023 AMC 8 Problem 20

Two integers are inserted into the list 3, 3, 8, 11, 28 to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?

\textbf{(A)} 56 \qquad \textbf{(B)} 57 \qquad \textbf{(C)} 58 \qquad \textbf{(D)} 60 \qquad \textbf{(E)} 61

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