I have limited knowledge of the Abbasid Caliphate, but from my general understand the Seljuks conquered the area and the caliph was just resigned to a ceremonial rule without much power. The sultan was the real person with power. So why the 11th century not viewed as the end? I'm just confused how Baghdad could be considered a part of two empires at the same time.
Like many things in history, this is the subject of interpretation. Many dynasties in history have had a similar destiny, being puppets and legitimizers of true rulers. However, the Abbasids didn't give up so easily. Caliph an-Nāṣir made a final attempt to restore the Caliphate to its original power: the Ayyubids of Egypt were preoccupied with the Crusaders, while the Khwarizm-shah was busy warring other Turkish dynasties. He did create a state of a sort around Baghdad and some parts of Persia, but in that he made the Khwarizm-shah his enemy, and only did the Mongol invasion save the caliph. Caliph an-Nāṣir descendants proved to be incapable of reviving the Caliphate, and when the Mongols led by Hulaku appeared in front of Baghdad (1258), Caliph al-Mustaʿṣim proved incapable of offering any true resistance.
So with that in mind, I'd say that 1258 is more suitable, if formal, end of the dynasty.