As ‘silvershredder’ says above concerning shared drains, however if your property was built pre Oct 1937 the Utility Co is responsible for maintaining drains.
We have had ours cleaned every two to three years and the issue is actually 50m away through next doors drains and out to where the sewer drains out to the road. If you had a similar issue there is no way you can DIY. These guys have industrial line, high pressure blasters and cameras to see where the issue it, what it is and cutting tools for roots.
Personally I would rod within your property, no attachments to start remembering to twist as you send it don and not how much distance you gain before any obstruction. if you do hit something and can release the blockage consider digging it up at some point and repairing whatever the issue is as it will reoccur within a few very short years.
If nothing is evident obviously within you grounds, talk to your neighbours and ask to lift a few manholes. to see where the problem may be. Try to determine whether you are on the end of a run and feeding into a shared drain. You can sort of do this by where you are located in the road etc. but it isn’t always apparent.
Then ring the utility company especially if you think it is a problem off your property or a public sewer. They should give you good advice.I’m waitin in today for them to return with a special cutting tool 🙂