Returning to SWTOR after a couple of years - Level 55 class quests?
Solution 1:
After level 50 there are no more class quests (apart from one very small one on Rishi around level 58).
Level 50-55 is Rise of the Hutt Cartel, as you've noticed, and presumably already done on your level 55 characters. It has one story per faction.
The next story expansion was Shadow of Revan from 55-60, which you can begin from a terminal your ship, and is partly faction-based but mostly a unified story.
After that are Knights of the Fallen Empire (60-65) and Knights of the Eternal Throne (65-70), which are entirely a unified story.