Just an easy simplification

31477313+713=abc \large 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + 7 \sqrt{ \frac{1}{3} } = \frac{a}{b} \sqrt{c}

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

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

This problem is a part of the sets - 1's & 2's & " N " for number theory.
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