the next Sunday

[sitifan]

I would visit you the next Sunday.

Is the above sentence acceptable?

[Raymott]

I would visit you the next Sunday.

Is the above sentence acceptable?

It depends. In what context do you want to use it? What is it supposed to mean?
It's obviously not complete in itself, because it's a conditional sentence without a condition. Can you write a short dialog in which you might use it?