Using proton-proton collision data at centre-of-mass energies of $\sqrt{s} = 7$, $8$ and $13\mathrm{\,TeV}$ recorded by the LHCb experiment at the Large Hadron Collider, corresponding to an integrated luminosity of $9\mathrm{\,fb}^{-1}$, the invariant mass spectrum of $J/ψ$ pairs is studied. A narrow structure around $6.9\mathrm{\,GeV/}c^2$ matching the lineshape of a resonance and a broad structure just above twice the $J/ψ$ mass are observed. The deviation of the data from nonresonant $J/ψ$-pair production is above five standard deviations in the mass region between $6.2$ and $7.4\mathrm{\,GeV/}c^2$, covering predicted masses of states composed of four charm quarks. The mass and natural width of the narrow $X(6900)$ structure are measured assuming a Breit--Wigner lineshape.