Question about shadow priest

I recently level to 60 and I geared my shadow priest with some shadow damage gear. My shadow spell damage is 140 (or 160 if I change weapon) but my mana is only 4800. At pvp my damage is good but I run out of mana very quick.
With this gear can I join lv 60 dungeon as dps or I will run also quick out of mana? I have to say that at AV I couldn't dps Drek because my SWP dot overwritten. I couldn't even use Mind Flay (because Mind Flay also needs a dot space for the slow debuff).
With this gear can I join lv 60 dungeon as dps or I will run also quick out of mana? I have to say that at AV I couldn't dps Drek because my SWP dot overwritten. I couldn't even use Mind Flay (because Mind Flay also needs a dot space for the slow debuff).