Oh boy!, here comes the Soothsayer

This problem can be solved through "Party Trick"

let's call the given number $a_{0}$ , which we got after division. i.e. $a_{0}=6.0131914894$ .

Now we apply Party trick.

$\left[a_{0}\right]=6.......................................................and$ $a_{1}=\frac{1}{a_{0}-\left[a_{0}\right]}=31.\bar3$

$\left[a_{1}\right]=31.....................................................and$ $a_{2}=\frac{1}{a_{1}-\left[a_{1}\right]}=3$

This methods End when we get an integer.

Now we apply the integral parts of all the value we got in the continued fraction like this

Let the fraction be Y, then $Y=\left[a_{0}\right]+\frac{1}{ \left[a_{1}\right] + \frac{1}{\left[a_{2}\right]}}$

Now substituting the values, we get: $Y=6+\frac{1}{ 31 + \frac{1}{3}}=\frac{567}{94}$

Now answer= $567+94=\boxed{661}$