Okay, I know the safe, kosher answer for OP's question is "No, you should not rely on herbal remedies in order to cure a cancer". Especially in the generic way the question is formulated, including the reference to "cure cancer" as if cancer was a specific viral disease instead of a vast complex.
But I'm going to be the odd one out here and add a couple observations. I'm not suggesting anyone to neglect clinical medicine for cancer treatment, but "cancer requires chemo/surgery" is not considering the fact that revolutionary developments over the last few years for cancer treatment are in immunotherapy, particularly immune checkpoint inhibitors and immunomodulators. And in both types of treatment, some of the most promising compounds are phytochemicals. I am not going to name examples because I don't want this thread to become a source of information that people might use to ignore clinical approaches, but there is a growing amount of biomedical research discussing specific plant compounds and extracts that are not only useful as a way of, for instance, minimize side effects in traditional chemotherapy, but useful as directly involved in the treatment itself. And I mean besides the unusual cases of remission related to the use of plant preparations, which are often accompanied by multiple other factors and thus can hardly be invoked as representing a "cure for cancer".
Should anyone avoid clinical medicine and try to treat their cancer using herbal preparations only? Definitely not.
Are there plants and plant extracts that can help treat cancer, beyond being a merely coadjuvant or supporting symptoms of other aggressive treatments? Absolutely yes, and if I ever get a diagnose, I expect to work with an oncologist that can include them in the treatment as well.