$AB = CD = 1$, $m\angle ABC = 90^\circ$, $m\angle CBD = 30^\circ$. $A$, $C$, and $D$, are collinear. $AC$ can be represented in the simplest form as $a^{1/b}$, where $a$ and $b$ are positive integers such that $a$ is minimized. Find $a + b$.

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