Let $p(x)$ be a cubic polynomial such that $p(-3) = 4,$ $p(-2) = 4,$ $p(4) = 4,$ and $p(5) = 16.$  Find $p(11).$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $p(x)$ be a cubic polynomial such that $p(-3) = 4,$ $p(-2) = 4,$ $p(4) = 4,$ and $p(5) = 16.$  Find $p(11).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
277
Let $p(x)$ be a cubic polynomial such that $p(-3) = 4,$ $p(-2) = 4,$ $p(4) = 4,$ and $p(5) = 16.$  Find $p(11).$
train