In this particular case, can I omit the "but" in a "Not only ... also" sentence construction?

I’ve looked at several threads about this, but I can’t really get a feel for whether or not this sentence in particular is correct:

Not only is it important for us to protect our own data, we also have
a responsibility to protect each other’s sensitive information.

Does the above sentence sound okay? It sounds like something I would say out loud, but I’m not sure whether it’s grammatically correct. Is it essential that I add the ‘but’ in there after the comma? Like so:

Not only is it important for us to protect our own data, but we also have
a responsibility to protect each other’s sensitive information.