Which cancer? There are hundreds and they're different. Different causes, different treatments required.
Although I suppose it's theoretically possible to have a generic whole-body treatment that somehow detects and kills all imperfect cells. That would cover all cancers, although it wouldn't be specifically targetting cancer. Maybe nanobots in blood could do it, theoretically. There have been recent breakthroughs in nanobots in vivo - scientists recently succeeded in making a way to power them.
I think that the next big breakthrough will be in batteries. That would be more important than it sounds, especially if it's very large scale batteries. There is some research going on that might lead to huge batteries with enough storage capacity to be of use on a national grid. That would be a game changer, making alternative means of electricity generation much more viable. Another direction with batteries that might happen in the fairly near future is a huge increase in charge to weight and charge to volume ratios, which would make electric cars much more viable.
Although the next
really big breakthrough might be economic nuclear fusion. A superabundance of very cheap, very clean electricity would have a lot of effects.
Going way out on a limb - a cure for aging. It's theoretically possible and it's hard to imagine something that would have more profound effects than everyone always being at the peak of adulthood and an average lifespan of centuries, maybe even millenia (people would eventually die from disease or injury).
Which leads me to think that my initial comments about cancer might be wrong. There might be a blanket cure for all cancers. Naked mole rats appear to be utterly immune to all forms of cancer and it appears to be related to their remarkable resistance to aging (they live about 6 times as long as would be expected and they spend almost all of it in the peak of adulthood).