Geometry Level 4

For $$\triangle ABC$$, the perimeter is $$\dfrac{29}{6}$$ and the products of the three sides is 4.

The circumradius and inradius of $$\triangle ABC$$ are $$R$$ and $$r$$ respectively.

If the quantity $$R \times r$$ can be written in the form $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers, find $$m+n$$.

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