Meaning: is there some characteristic of all cancers, that makes it likely that a single treament would cure it?
As I understand it, cancerous cells divide much faster than normal cells. Suppose we find a substance that can be taken up by cancerous cells, and kills them. Would this work for all cancers?
Might depend on your definition of ‘work’ - as I understand it, chemotherapy is based on that principle, and it’s generally capable of killing any cancer. The problem is that it tends to kill non-cancerous cells as well. 
(That may be a tremendous simplification I know.)
I can almost foresee a future in which nanotechnology might be able to selectively kill cancer cells of many or perhaps all forms. Maybe.
Suppose we find a substance that can be taken up by cancerous cells, and kills them
I am not sure about a"substance" but the same process might work as a magic bullet. It is one I think will come in a decade that the younger members of this board might very well live to see toward the ends of their lives.
I’m referring to Gene Therapy where we may see this:
We might be able to develop a process to turn off of the dividing cancer cells. I would imagine theoretically, that it might be the same, or for all intents and purposes the same, process done for all cancers. Obviously, each specific kind of cancer would require different genes be shut off using the same process.