If a planet of radius $R$ spins with an angular velocity $\omega$ about an axis through the North Pole, find the ratio of the normal force experienced by a person at the equator to that experienced by a person at the North Pole. Assume a constant gravitational field $g$ and that both people are stationary relative to the planet and are at sea level. The original answer is in the form $k - \frac{mR\omega^2}{ng}$, please give the value of k + m + n.

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