A regular hexagon with sides of length $6$ has an isosceles triangle attached to each side. Each of these triangles has two sides of length $8$. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid? Express your answer in the form $a\sqrt{b}$, where $a$ and $b$ are integers. Please provide the value of $a + b$.

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