The most famous myth in the history of Western philosophy, the myth of the cave, was written by Plato 2500 years ago.

Myth of the Cave seems to be an accepted name for what you're discussing (I've only ever heard Allegory of the Cave), and I've never studied philosophy, but I would probably at least exchange the first instance of "myth" for another word? "Myth" usually makes me think of mythology.

In this myth, some men are locked in a Ccave and can only see shadows, which they consider to be real objects .

One day, one of them manages to go out and, after much effort, understands that the true reality is what is outside of the cave.

One of the most relevant is the idea that in order to acquire true knowledge oneeds effort to be found must put in effort.

I don't think relevant is the word you're looking for. Maybe widely-accepted/common/well-known. The second half of your sentence was a little too abstract.

Well, Fake Nnews is not true knowledge, despite what many people believe.

This is the reason why the European Commission has a group of experts twho study how to locate Fidentify fake Nnews and how to fight it.

However, this conviction that it is possible to separate the truth from 'what appears to be true' is an idea was advanced by Plato more than 2000 years ago.

You already call it a conviction, no need to also call it an idea.

Both, the European Commission and Plato, give the same solution: study more closely the information that reaches us.