If $x$ is a number satisfying the equation $\sqrt[3]{x+9} - \sqrt[3]{x-9} = 3$, find the value of $x^2$ and determine which interval it falls into among the following: $[55, 65]$, $[65, 75]$, $[75, 85]$, $[85, 95]$, $[95, 105]$. The original answer is in the form $[a, b]$, please give the value of $a + b$.

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