It's correct in my opinion.
Considering talked to/with and spoke to/with,
I think that "talked" has more of a sense of conversation than "spoke" does. That is, it suggests a meeting of the minds.
However, "spoke" would not be incorrect, especially since you have specifically stated that there was a meeting of the minds. But in either case, I think I'd be inclined to use "with."
There have been other threads on this subject, and they always seem to generate a lot of controversy as to the differences in usage.