If $57a + 88b + 125c \geq 1148$, where $a, b, c > 0$, what is the minimum value of
\[
a^3 + b^3 + c^3 + 5a^2 + 5b^2 + 5c^2?
\]

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