Side $AB$ of regular hexagon $ABCDEF$ is extended past $B$ to point $X$ such that $AX = 3AB$. Given that each side of the hexagon is $2$ units long, what is the length of segment $FX$? Express your answer in simplest radical form.The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

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