Do you agree that "6", "six" and "VI" are the same number? They represent the same thing, after all.

In much the same way, "6+3=9", "six plus three is nine" and "VI+III=IX" are all the same equation, just with a different look. They all *mean* the same thing, though. Even though the number systems don't even have the same structure! One is a positional notational system, one is based on words, and one is based on god knows what the Romans were thinking when they invented that. Still, the algebra is the same because all three systems are used to represent something more overarching, more abstract: numbers are something with inherent meaning, they're not just a string of symbols. Algebra is about numbers, not about their representations on paper or on a screen. So the algebra doesn't change when changing the number system, even if the systems bear no resemblance at all. And the same is doubly true for number systems which are structurally similar, like a base 10 and a base 11 system.