"'to do' something" and "doing something" are completely equivalent. The former is the infinitive, and the latter is the gerund form. Both work, whether preceded by "like" or "dislike".

I like doing something.

I like to do something.

I dislike doing something.

I dislike to do something.

Just don't say:

I like to doing something

"'to do' something" and "doing something" are functionally equivalent in this case. The former is the infinitive, and the latter is the gerund form. Both work, whether preceded by "like" or "dislike".

1. I like doing something.

2. I like to do something.

3. I dislike doing something.

4. I dislike to do something.

The last example (dislike +inf.) is awkward and rarely used, but still grammatically correct.

Just don't say:

I like to doing something