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

where \( a \) and \( b \) are positive co-primes and \( c \) is not a perfect square .

Find \( \large a + b + c \) .

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