You can change the dash pattern in Inksape's XML Editor
Make sure you have the object selected first and make sure you already added a dash in the Fill & Stroke panel's Stroke Style tab, then open the XML editor Shift+Ctrl+X
Select the Style attribute to edit it, and look for the a piece of code that looks like this.
The numbers shown may be different for you depending on what dash you selected. But the default is two numbers separated by a comma.
You can edit these numbers, and after you've done it, hit the check mark button in the XML
In the example below, I set it to a dash of 10, followed by a gap of 5, then a dash of 15, then a gap of 5. You can have more numbers if you want a more complex pattern. Here's what it looks like after I edited it.
After doing this you will almost certainly have one dash/gap that is longer than it should be, as you can see in the above example. You can fix this by very slightly adjusting the stroke width until it looks right.
Edit Further to the comments
A more accurate method might be to create a pattern using a grid, 360mm long (1mm per degree). Then you could accurately measure the gaps and lines. These lines are actually made of filled rectangles. Snapping will enable you to draw the rectangles so the fit the grid exactly.
Then combine these as one path (using Path > Combine)
Copy it, then apply as a pattern along a path to a circle using the Link Path to Clipboard button, and the Single Stretched option in the Path Effects dialog
Note: the first and last rectangles are 10mm, both together making a 20mm rectangle when joined together in the final path effect.