There are a few mistakes in the sentence (which I guess you made because you transcribed it as you heard it) but we can forget them. In particular, pero que no se te pueden olvidar should be pero que no se te puede olvidar (with puede in the singular, agreeing with algo).
The verb olvidar can be used in several different ways. There's a so-called pronominal form of the verb, olvidarse, where -se stands for a reflexive pronoun which refers to the subject. The subject is the one who forgets. The verb can either be transitive (with a direct object), or intransitive with an optional complement preceded by the preposition de:
- Me olvidé (de) todo. "I forgot (about) everything."
- No te puedes olvidar de ella. "You cannot forget about her."
This is the pattern that you think you saw, but it's not what you are seeing in no se te puede olvidar. You know this is not the case because if it were, the main verb would be in the second person, agreeing with the second-person pronoun te, just as in me olvidé and te puedes in my two examples above.
So this is a different pattern. It's another pronominal form and it's basically intransitive; here, unlike the other form, the subject is the thing being forgotten. In English you would render it as a passive voice. Some examples:
- Una cosa así no se olvida. "Something like that is not forgotten."
- Las fechas se olvidan fácilmente. "Dates are easily forgotten."
The pattern you found (no se te puede olvidar) is the above plus a dative (an indirect object). The subject is still the thing being forgotten but the indirect object allows you to specify who does the forgetting; in English you could render that with "by":
- Una cosa así no se te olvida. "Something like that is not forgotten by you."
- Las fechas se me olvidan fácilmente. "Dates are easily forgotten by me."
But this is rather clumsy; in reality you would rather say (with a fronted direct object):
- Una cosa así no se te olvida. "Something like that you don't forget."
- Las fechas se me olvidan fácilmente. "Dates I don't easily forget."
The grammar is puzzling but you can find some parallels. This form (olvidarse + indirect object) works a bit like gustar, where the subject and indirect object are swapped from the English perspective. Also, olvidarse is not the only verb that works like this; morirse, romperse and a few more work like that, with pairs of alternative patterns where subject and indirect object can swap positions. One pattern focuses on the agent, generally an animate being (the one who forgets, dies or breaks something), while the other focuses on the patient, generally a non-living entity (the thing being forgotten, the thing dying under someone's care, or the thing that is broken).