The correct translation of "zusammenlernen" in this sentence is "to study together" rather than "to learn together". If a German student of English said "we learned together" a native speaker would immediately find the sentence odd.
In German "lernen" means to study, as in to study for a test. No body would ever say in English "we learned together"
You might say "we learned together." "I learned that today." "We learned it together." It just doesn't mean quite the same thing as "we studied together."
In English we DO say "we learned together." It just doesn't necessarily mean "we studied together."