"I live on the longest road."
Translation:저는 제일 긴 길에 살아요.
It should be 길에.
~에서 – where an action takes place.
~에 – where something static is happening
The word live in that case means something static as for example the house you live in. So to paraphrase it: My house is located on the longest road.
You can actually use both 에 and 에서 in this case. You can use the static locative particle (에) and the dynamic locative particle (에서) when you use the verb 살다.
저는 미국에 살아요=저는 미국에서 살아요 (I live in the US)
Though there is a very subtle difference in meaning, both sentences can be used interchangeably.