The left side casing is dead easy to remove and take a look. Only need to remove the gear lever linkage with a 10mm spanner, then 4 x 5mm caphead screws.
Broken output shaft sounds a bit odd, could it be the sprocket nut has failed? with the left casing removed you'll be able to see/touch it.
Or possibly something has happened to the clutch basket on the right side?
If either gearbox shaft is damaged it's an engine out and split job. If it's a clutch issue that's a lot easier to sort.