With almost 5000'/min rate it takes a little more than 4 minutes to get down from F360 to 14000'; it's not such a long time to... "Aviate, navigate, communicate" & "Dive and drive"!!!
How expeditious does the descent need to be after loss of cabin pressure? There will be at least 10 minutes' worth of oxygen for pax and crew (and probably more for the pilots). A quote from
'How To Do Well In The Sim':
<<When you call 'MAYDAY', if you can get some sort of ATC clearance before you plummet, so much the better. It would be pointless doing the drill perfectly and then slamming into another aircraft beneath you on the way down. The TCAS telling you 'CLIMB . . . CLIMB' won’t be much use at this point. The question is: 'how long do I spend trying to get an emergency descent clearance?' And of course no-one can give you an answer – you must use your judgement as to when to start down if ATC can’t help. However, remember you've got 12 minutes of passenger and cabin crew oxygen available and considerably more for the pilots. If you stay aloft a short time while you get a clearance and then descend at current IAS (in case of damage) you'll still have plenty of time to get down to breathable air before the oxygen runs out.
One of the difficulties in this scenario is communication with cabin crew – they can't talk to you with their masks on, so it's one way traffic only. Having done the QRH checklist you could do a combined PA for both the cabin crew and the pax, along the lines of: '. . . we've lost cabin pressure, so everyone make sure you've got your oxygen masks on . . . cabin crew stand by for further instructions . . .'. At the end of the descent your PA could be '. . . cabin manager, take off your mask and report to the flight deck . . .' Or if for some reason you need to talk to the cabin manager during the descent, you could tell him on the PA to don a portable bottle and report to the flight deck. He can then listen to what you say over the speaker.>>
The 12 minutes refers to the B757/767 but I would expect other aircraft to have similar oxygen endurance.