The solutions to the equation \((z+6)^8=81\) are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled \(A,B,\) and \(C\). Find the least possible area of \(\triangle ABC\). The original answer is in the form \(\frac{k}{m}\sqrt{n} - \frac{k}{m}\), where k, m, and n are integers. Please provide the sum of k, m, and n.

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