Let $a,$ $b,$ $c$ be distinct integers, and let $\omega$ be a complex number such that $\omega^3 = 1$ and $\omega \neq 1.$  Find the smallest possible value of
\[|a + b \omega + c \omega^2|.\]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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