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To solve the equation \( 5m - 2m + 6m = -81 \), first combine the like terms on the left side:
\[
(5m - 2m + 6m) = (5 - 2 + 6)m = 9m
\]
Next, the equation simplifies to:
\[
9m = -81
\]
Now, divide both sides by 9 to solve for \( m \):
\[
m = \frac{-81}{9} = -9
\]
Thus, the solution is:
\[
\boxed{-9}
\]