Let the positive numbers $a _ { 1 } , a _ { 2 } , a _ { 3 } , a _ { 4 }$ and $a _ { 5 }$ be in a G.P. Let their mean and variance be $\frac { 31 } { 10 }$ and $\frac { m } { n }$ respectively, where $m$ and $n$ are co-prime. If the mean of their reciprocals is $\frac { 31 } { 10 }$ and $a _ { 3 } + a _ { 4 } + a _ { 5 } = 14$, then $m + n$ is equal to $\_\_\_\_$ .