If you use I(V1), you get the magnitude of the current.
So if you plot I(L1)+I(R1)+I(C1) you plot the sum the magnitudes.
Using the magnitude ignores the phase differences between the currents, the imaginary part of the current is removed and converted into the magnitude value.
Only if you would do a "proper" sum of I(L1)+I(R1)+I(C1) that takes into account the imaginary part of the currents and plot the magnitude of that sum, would the result be the same as I(V1).
When you plot I(V1) the summation is done properly (taking the imaginary part, phase etc) into account. So then at the resonance frequency, the inductor and capacitor's impedances cancel each other out and "from the outside" (looking at the impedance of the RLC tank) you only see the impedance of the resistor.
Tip: you're now actually plotting the admittance 1/Z. If you want the impedance plot, print 1/I(V1) or do as I usually do: replace the AC voltage source V1 with an AC current source with AC = 1. Then the voltage at "input" is the same as the actual impedance as V = I * Z = 1 * Z = Z (I = 1 because of the current source with AC = 1).