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$\large 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + 7 \sqrt{ \frac{1}{3} } = \frac{a}{b} \sqrt{c}$

where $a$ and $b$ are positive co-primes and $c$ is not a perfect square .

Find $\large a + b + c$ .

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