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\date{\today}  Within the diquark-antidiquark model the masses of the $0^{++}, cc\bar c\barc$ resonances are calculated, using the expansion of the four-quark wavefunction in the set of the hyperspherical functions. The interaction is definedvia a universal pair-wise potential, which does not contain fitting parameters.The resulting masses $M_4(nS)$ are shown to be very sensitive to the value of$c-$quark mass, chosen in relativistic string Hamiltonian, and $m_c=1.24, 1.30,1.43$ (in GeV) are considered. The choice of $m_c$, equal to the current mass,$m_c=1.245$ GeV, yields three $nS~(n_r=0,1,2)$ states in a very good agreementwith the masses of the $X(6550), X(6900), X(7287)$ resonances, if thegluon-exchange interaction is totally neglected. This fact indicates on apossible screening of the gluon-exchange interaction inhe $cc\bar c\bar c$system. For $m_c=1.43$~GeV the ground state mass $M_4(1S)=6557$~MeV is obtainedin agreement with experiment only if $\alpha_{\rm V}\cong 0.39(1)$ is used,however, in this case the masses of the $2S, 3S$ radial excitations exceed themasses of $X(6900), X(7280)$ by $\sim 100$~MeV.

The $X(6550), X(6900), X(7280)$ resonances as the $nS, cc\bar c\bar c$ states