Looking on the internet deeply has found these results:

I like to read book and travel. is the most popular phrase on the web.

I like to read book and to travel. 10 results on the web	I like to read book and travel. 11 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Learn Chinese in Beijing, Study Mandarin in China, Chinese classes.

I like to read book and to travel.

10 results on the web

I like to read book and travel.

11 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.