the difference here is actually a subtle difference in the use of "would" In English, we often use auxiliary verbs expression condition/possibility like would/could/may/might as formalities in order to express politeness. "I would like to travel" uses this as it actually means "I want to travel." "I would like traveling" actually expresses the conditional meaning of "would" here, to mean "If it were possible" or "If the opportunity arises" "I'd like traveling." also expresses the lack of the experience meaning that you have not traveled before. These are my observations, tho I unfortunately do not have a good explanation for why the differences exist. I hope, however, that this helped clear things up a little :)

It should be: 'I'd like to travel- I would like to travel (I'd is just an abbreviation) 'I like travelling'- the above sentence is about you wanting to travel, possibly for holiday. Where as this sentence is about you liking 'travelling' in general: suggesting that you like going abroad on holidays. Hope i could help :)