I want to know if i switch into Sport mode, can I travel longer distance, rather than regular mode?

No, you can neither travel further nor farther.  

You can travel further quicker, but not farther.

Only a lot faster

It's also worth noting that Sport Mode disables the front sensors.

Flying rather than hovering apparently gives you longer time in the air due to hovering taking more power from the batteries to enable it to stay still.  Therefore in some circumstances I would suggest that moving at an optimum speed will enable longer battery life and further(farther) distance.  I would say that potentially this could be achieved in sports mode, in my opinion.

Someone here worked out/suggested an optimum speed of say 22mph, which can be achieved in normal mode, therefore it could also be achieved in sport mode. The propensity to use more power is limited in normal mode, so it could be considered a good safeguard to use normal mode in case you get heavy on the sticks in sport mode. However, real world situations change as to the amount of resistance the drone encounters such as wind speed and to a lesser extent humidity.
A headwind that exceeds the top speed of the Mavic in normal mode will mean the drone will be travelling backwards relative to the ground. In such a case, or if it's making poor headway, then sport mode may be the only guarantee of it making it back "home".

I've heard (unsubstantiated) that you can fly around the globe in sport mode with the optional solar array. The forward sensors are disabled to watch for hidden obstacles.