If you fit a wider wheel, you have to be careful how much further in the inner edge is, as this can contact the suspension or car body.
The ET35 is how far the mounting face is offset from the centreline of the wheel. As an example, my 5.00" rims (127mm) with a 35mm offset puts the inner edge of the rim about 98.5mm in from the mounting face.
With the proposed 6" rims (152mm), with the same 35mm offset, puts the inner edge 111mm in from the mounting face. So you need at least another 12.5mm clearance.
The outer edge will also be further out, by the same 12,5mm, so clearance to the arches may be an issue, especially when turning. The tyres must also be within the width of the car, so must not protrude beyond the bodywork.
The offset not only puts the wheels in the right place in relation to the bodywork, it is also intended to place the centreline of the wheel close to the centreline of the bearings. With the ET the same, this should be fine, but if a different ET is chosen to obtain the clearances needed, bearing stresses may become a problem. (Original Minis were often fitted with wheel spacers, which shortened the life of the front wheel bearings by about a third.)