how to sovle x^3 = a mod p ,where is p is prime, a is known. how to sovle it with PARI/GP/pg

Question

when a solve

x^3 = 11826493364627776165 mod 17178964373573894299

there are 3 solution [8385928023199723804,11846820199768219252,14125180524179845542]

when i use PARI/GP i only get 1 solution as

? b=Mod(11826493364627776165,17178964373573894299)^(1/3)


%30 = Mod(8385928023199723804, 17178964373573894299)

the output of PARI/GP

how to sovle it?

Answer 1

Here's a possibility:

a = Mod(11826493364627776165,17178964373573894299);
x = sqrtn(a, 3, &j);
lift([x, x*j, x*j^2])