Let $Q$ be a polynomial \[Q(x)=a_0+a_1x+\cdots+a_nx^n,\]where $a_0,\ldots,a_n$ are nonnegative integers.  Given that $Q(1)=4$ and $Q(5)=152$, find $Q(6)$.

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