In the $xy$-plane, consider the L-shaped region bounded by horizontal and vertical segments with vertices at $(0,0)$, $(0,3)$, $(3,3)$, $(3,1)$, $(5,1)$, and $(5,0)$. Find the slope of the line through the origin that divides the area of this region exactly in half. The original answer is in \(\frac{k}{m}\) format, where \(\frac{k}{m}\) is a simplified fraction. Please give the value of \(k + m\).

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