Root.m

Root[-1 + 30 # + 170 #^2 + 672 #^3 - 6956 #^4 - 6808 #^5 + 42872 #^6 - 56576 #^7 - 241616 #^8 + 712800 #^9 + 
   1099296 #^10 - 2718208 #^11 - 3427264 #^12 + 5028992 #^13 + 8030592 #^14 - 3956736 #^15 - 14783232 #^16 - 2065920 #^17 + 
   20241920 #^18 + 7954432 #^19 - 19317760 #^20 - 7817216 #^21 + 12445696 #^22 + 3342336 #^23 - 5435392 #^24 - 122880 #^25 + 
   1662976 #^26 - 393216 #^27 - 344064 #^28 + 98304 #^29 + 32768 #^30 &, 4] == 
With[{α = 1/5 ArcCos[(255300649 + 251245525 Sqrt[5])/(4 * 11^8)], β = Sqrt[25085 - 6802 Sqrt[5]]},
 With[{κ = 11 β Sin[α], λ = β Sin[2 α], μ = 11 * 811 Cos[α], ν = 811 Cos[2 α]},
  With[{η = 11^3 * 811 (55 - 14 Sqrt[11]) - 
      11 κ (2474 + 1479 Sqrt[5] - 763 Sqrt[11] - 385 Sqrt[55]) + λ (22127 + 140925 Sqrt[5] + 3421 Sqrt[11] - 35431 Sqrt[55]) - 
      11 μ (365 + 38 Sqrt[5] - 107 Sqrt[11] - 9 Sqrt[55]) - ν (39510 - 14118 Sqrt[5] - 12837 Sqrt[11] + 3179 Sqrt[55]),
    ρ = 11^3 * 811 (Sqrt[11] - 3) + 
      4 κ (1397 + 132 Sqrt[5] - 466 Sqrt[11] + 122 Sqrt[55]) + λ (46291 + 43551 Sqrt[5] - 9923 Sqrt[11] - 9501 Sqrt[55]) - 
      2 μ (638 + 22 Sqrt[5] - Sqrt[11] - 63 Sqrt[55]) + ν (5479 - 3061 Sqrt[5] - 4723 Sqrt[11] - 1341 Sqrt[55]),
    σ = 2 * 11^3 * 811 (11 - 2 Sqrt[11]) - 
	  κ (13673 - 2431 Sqrt[5] - 4514 Sqrt[11] - 120 Sqrt[55]) - λ (172406 + 140252 Sqrt[5] - 23673 Sqrt[11] - 31171 Sqrt[55]) + 
	  μ (3179 + 143 Sqrt[5] - 798 Sqrt[11] - 180 Sqrt[55]) - ν (15896 - 1642 Sqrt[5] - 6967 Sqrt[11] + 1035 Sqrt[55])},
        With[{τ = 2 * 11^3 * 811 (20 Sqrt[11] - 33) + 6 * 11 Sqrt[3 * 5 * 11 * 811 η] + 
	          κ (166573 + 3025 Sqrt[5] - 49167 Sqrt[11] - 2979 Sqrt[55]) + 
            2 λ (576143 + 229934 Sqrt[5] - 195022 Sqrt[11] - 64418 Sqrt[55]) + 
			      μ (2453 - 2035 Sqrt[5] - 505 Sqrt[11] - 113 Sqrt[55]) + 
			      ν (292348 + 26650 Sqrt[5] - 75990 Sqrt[11] - 2062 Sqrt[55])}, 
    1/(2 * 3 * 5 * 11^3 * 811) (ρ + 11^2 * 2^(1/3) * 5^(2/3) * 811^(2/3) * τ^(1/3) + 11 * 2^(2/3) * 5^(1/3) * 811^(1/3) * τ^(-1/3) * σ)]]]]