To add to Charlie's answer, we also use 'work at' with company names, and places. e.g. I work at Google, or I work at the steel refinery. You can't use 'on' with those. Conversely we 'work on' things, e.g. I am working on my lawn mower, and Biologists are working on a cure for dieback. We would not use 'at' for those.

You could certainly substitute "work on" for "work at" in the sentence you have given without changing the meaning much, if any. I don't think you can always use the terms interchangably, however. To "work at" something implies a long-term project that can't be completed quickly, or ever. For example, if I struggle with being overweight, I might say: "I really have to work at keeping my weight down." On the other hand, you can "work on" something as short-term as a paper for school or cleaning one's house, both of which can be accomplished in the near future.

In the context of making an effort over time, I would use "work at [doing something]" with a goal or target in mind. The phrase "work on" suggests improving your skill for an activity through practice and repetition.

In that sentence they are pretty much interchangeable, but you could say “I work at apple. While I’m there I work on computer chips.” and they would not be interchangeable.