# Hard Sequence of Fractions

Algebra Level 3

$${\frac{6}{3}, \frac{18}{21}, \frac{m}{n}, \frac{32}{67}, \frac{42}{99}, \frac{a}{b}}$$

$${m}$$ $$\in$$ {m is a positive integer | $${\frac{1}{3}(m(4-\frac{1}{3})+(\frac{1}{4})^{-\frac{3}{2}}) = 32}$$}

$${n}$$ $$\in$$ {n is a prime, positive integer | $${39 < n < 51}$$}

The fraction $${\frac{a}{b}}$$ is the 6th term, it is in its simplest form.

Find the value of $${a+b}$$.

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