While exploring a cave, Carl comes across a collection of $5$-pound rocks worth $14 each, $4$-pound rocks worth $11 each, and $1$-pound rocks worth $2 each. There are at least $20$ of each size. He can carry at most $18$ pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?

Let's think step by step and output the final answer within \boxed{}.
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