If \(a, b, c>0\) and \(a+b+c=1\),
the minimum value of
\((a+\frac{1}{a})^{10}+(b+\frac{1}{b})^{10}+(c+\frac{1}{c})^{10}\) can be expressed as
\(\frac{10^{d}}{3^{e}}\) where \(d\) and \(e\) are positive integers.
Find \(d+e\)

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