I'd say that in OP's example, plural bananas refers to "bananas in general" and "more than one banana" simultaneously, just as Monkeys like a banana simultaneously refers to "bananas in general" and "one single banana".
The third possibility is Monkeys like banana (singular, no article), which doesn't really refer to "bananas in general" - it uses banana as a "mass noun", meaning that monkeys like the substance (or flavour) known as banana.
In principle (but probably not in practice! :) a particular monkey might like a banana (or equivalently he might like bananas) provided you offer him the whole fruit. But he might not like banana if you gave him some banana pulp mashed up in a bowl, or offered him a banana milkshake.
There's no equivalent to that third possibility with OP's good institutes example. In almost all contexts, there's no difference in meaning between...
1: Studying at good institutes can really make a difference.
2: Studying at a good institute can really make a difference.
...but idiomatically #2 is much more common.
The idea of an individual student studying at multiple institutes (concurrently or consecutively) is culturally unfamiliar to me as a Brit, which is why I find it hard to imagine any difference in meaning between #1 and #2 above. But noting a solitary unexplained downvote, I'll try to explain in more detail how "plurality" works in such contexts by switching to a slightly different example...
3: Blood serum levels of DDT in these children were significantly correlated with duration of nursing, having older mothers, and residing in a rural area.
...which is perfectly valid, both logically and grammatically. But it would mean exactly the same with the singular form having an older mother and/or plural residing in rural areas.
I'm quite certain "these children" referred to in the above study came from more than one different "rural area", though obviously each individual child has only one mother, and comes from one area. But neither the above author nor myself has any problem with including both singular and plural references in the same sentence.
From this perspective, it should be clear that OP's "institute" example can quite naturally be understood as referring simultaneously to all/any good institutes and a single institute as normally attended by any given student.
As has been pointed out by @Daniel Warke, if the point OP really wanted to make was that each individual student must study at multiple institutes in order to gain the advantage, this would need to be explicitly stated. If not, that somewhat "perverse" interpretation would probably be missed.