Едем на работу = we are going (by car, bus, train, metro etc ) to the work

Идём на работу = we are walking to the work

That means to go to work by any means of transportation. For example, by car, by bus, by train and so on. So, it's like "let's go to work".

Does it make sense?

https://ru.wiktionary.org/wiki/ехать

Вот ещё хороший клип - и "ехать" есть и главное русское ругательство :-)

https://www.youtube.com/watch?v=AQqiUusn04k