The expression $\left(1 + \sqrt[6]{26 + 15\sqrt3} -\sqrt[6]{26 - 15\sqrt3}\right)^6= m + n\sqrt{p}$ , where $m, n$, and $p$ are positive integers, and $p$ is not divisible by the square of any prime. Find $m + n + p$.

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