A common tangent $T$ to the curves $C _ { 1 } : \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ and $C _ { 2 } : \frac { x ^ { 2 } } { 42 } - \frac { y ^ { 2 } } { 143 } = 1$ does not pass through the fourth quadrant. If $T$ touches $C _ { 1 }$ at $\left( x _ { 1 } , y _ { 1 } \right)$ and $C _ { 2 }$ at $\left( x _ { 2 } , y _ { 2 } \right)$, then $\left| 2 x _ { 1 } + x _ { 2 } \right|$ is equal to $\_\_\_\_$ .