[one month] and [one week]

[ansonman]

I have made up the sentences below.

(1) I travel a lot. One month, I went to Europe to visit my friend and found out that he got married.

(2) I have been an insurance sales clerk for five years. I remember that one week, I was not able to get any clients. That was the worst time of my career.

My non-native friends think "one month" and "one week" are ungrammatical.

Are "one month and one week" wrong? Thank you for your help.

[Alan]

Both are possible.