This is a matter of Ijtihad as our leading scholars have different verdicts on it. Ayatullah Khoei and many other scholars say that moon sighting in any part of the world is enough for all parts which shre night with that place. Ayatullah Sistani and many other scholars say that moon sighting depends on the area of sighting and nearby places which share the same horizon.
You need to follow your Marje' of Taqleed.
Laylatul Qadr will follow the date of the start of the month of Ramadan.
Wassalam.