Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.