Phone switching problem

Hello everyone, I recently switched from Nexus 4 to Nexus 5X, due to the fact that my Nexus 4 screen got another crack, and I didn't feel like fixing it, again. However, when I made the switch, I lost one of my games, "Megapolis", I didn't lose the app, I still got it, but I lost everything I built in the game, and I have to start from the start, again. Why? I don't know, but I am upset, because while it is just a game, I did spend a lot of time & quite a few $$$. I am hoping someone here could help, and was wondering if there's still a chance to fix that issue. I am planning to fix the screen myself. Also, I will say that my neither my Nexus 4 nor Nexus 5X are rooted. I am planning to root the 5X, maybe even the 4, if I can fix the screen.
Please & Thank You.

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