I don't agree with this advice at all. Do the work you're paid to do - no more, and no less. In my experience, working extra doesn't actually get you more respect from an employer. Often times, it's the opposite.
Back when I was working as salaried employee, I never asked for a promotion or a raise. Not once. But I got them! Meanwhile, I watched coworkers spend years fighting for promotions, taking on so much more work than I would ever agree to, and were repeatedly denied. Eventually, they would give up and get a job elsewhere. Some did manage to get promoted, but it was grueling.
These coworkers weren't less skilled than I was. I would say many of them were actually more capable, despite my position being ranked higher.
A lot of comments here are talking about "healthy" work cultures and whatnot. I worked for medium-sized tech companies that you've heard of with great engineering cultures and a healthy approach to work-life balance. I don't believe that "healthy" results in getting recognized for going above and beyond.
Others are mentioning office politics. I did not befriend coworkers, did not make enemies, etc. I simply did my work.
I'm sure many of you have had the experience that if you make a mistake—not necessarily at work, but just in general—and then apologize profusely, you will be treated worse than if you were more casual or didn't even apologize at all. I find that making yourself "smaller" will often result in people taking advantage of you. Similarly, it seems to me that working super hard will simply raise people's baseline expectations of you, and they will exploit that. This isn't necessarily a conscious thing on behalf of your boss(es), but it's absolutely something that happens.
Given all of that, my advice is to simply do your job. Over time, you will gain more experience, and that experience will potentially turn into promotions naturally. If not, then get a new job. Note however, that I'm not a proponent of frequent job hopping (I never spent less than three years at a company).
If you're not self-employed, then your work is making someone else rich. No need to make them even richer if you're not getting compensated for it.