Lisa has given you sound advice, pun definitely not intended.
Nylon string guitar tone is mellow compared with the brightness of a steel stringed acoustic. Perhaps you are aurally interpreting this as "bassy".
Cheap' isn't technically qualitative though. It'd be helpful to know what you actually have. Link, image, or brand, model. The most common nylon string guitars still today are conventional Classical. If it's a cheapie, this is likely what you have.
I'm not a guitar snob by any stretch. A decent enough Classical guitar which won't be a limiting factor for a long time in the process of learning to play needn't be expensive. e.g. Yamaha C40, Cort AC100. That said, at the bottom of the cheap barrel there is some utter rubbish out there with hotglued MDF bodies which will sound dull no matter the quality of strings fitted.
Hadn't heard of Adagio strings until I read of them here. Never one to dismiss something unfamiliar out of hand, they receive overwhelmingly positive reviews on Amazon UK where they appear to enjoy popularity.
As for nylon string recomendations? From the modest selection I've used to date, I prefer either D'Addario Pro-Arte EJ-45 or Alice AW130N on my Classical. Both Normal tension. Two ends of the price spectrum due manufacturing origin, they're both excellent in class. I can recommend either with confidence. I prefer to pay for AW130Ns.