Two squares, with integer side lengths $a$ and $b$, are arranged so that one entire side of the smaller square overlaps a part of a side of the larger square, and the two squares share a vertex, as shown. The perimeter of the entire figure is $86 \text{ cm}$, and the sum of the areas of the two squares is $386 \text{ cm}^2$. In centimeters, what is the value of $a+b$?
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