Is it worth putting a 1 month job on my CV?

yksi

Just as an add-on - you do not have to include everything on your CV in the first place and it's not about being dishonest. In fact your CV should be tailored to the job you're going for. So you want more detail in the positions most relevant and less detail in the ones that just filled time in your life. And you also want to include relevant qualifications but might choose to leave out your Food Hygeine Certificate if you're going for a job in a bank.