Amongst many uses, the word "one" is used as a pronoun to refer to someone or something (countable) of the type already mentioned.
As for the word "another", it can be used as a pronoun or a determiner.
When used with the pronoun " one", it's a determiner.
You use the word another as a pronoun or determiner in the following senses:
1.To refer to one more ( additional) of the same type as mentioned before. For example, I have had a cup of tea. I want to have another (pronoun). I have had a cup of tea. I want to have another (determiner) one (pronoun used instead of a cup of tea).
2.To refer to someone or something different to the type mentioned before. For example, I don't like a white shirt. Please show me another (pronoun).
I don't like a white shirt. Please show me another (determiner) one (pronoun). Here you mean a different shirt, not white one.
In light of the explanation #2, I think you can either use one or omit it in the sentence presented by the OP, without any difference in meaning. The use of another without one is as a pronoun, and the use of another before one is as a determiner while "one" is a pronoun.